Suppose, we have a problem of minimization of a function of scalar variable:
Sometimes, we refer to the similar problem of finding minimum on the line segment :
Line search is one of the simplest formal optimization problems, however, it is an important link in solving more complex tasks, so it is very important to solve it effectively. Let’s restrict the class of problems under consideration where is a unimodal function.
Function is called unimodal on , if there is , that and
Let be unimodal function on . Than if , then: